Prime, composite and fundamental Kirchhoff graphs
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math.CO
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kirchhoffgraphsgraphprimealgorithmexistencefundamentalmultiplicity
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A Kirchhoff graph is a vector graph with orthogonal cycles and vertex cuts. An algorithm has been developed that constructs all the Kirchhoff graphs up to a fixed edge multiplicity. This algorithm is used to explore the structure of prime Kirchhoff graph tilings. The existence of infinitely many prime Kirchhoff graphs given a set of fundamental Kirchhoff graphs is established, as is the existence of a minimal multiplicity for Kirchhoff graphs to exist.
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